Windowed Green function method for acoustic and electromagnetic wave scattering by periodic media

This work introduces a novel boundary integral equation (BIE) method for the numerical solution of time-harmonic acoustic and electromagnetic scattering problems in the presence of periodic media in two and three dimensions. We consider both 1d- and 2d-periodic infinite arrays of bounded penetrable scatterers. Our approach is based on the windowed Green function method [1], and it relies on a direct BIE formulation using the free-space Green function instead of the quasi-periodic one. The resulting BIE system involves integrals over the (unbounded) unit cell’s boundary. Such integrals are approximated via window integration that introduces errors that decay super-algebraically fast as the window size increases. The resulting second-kind BIE system is then discretized using a Nyström-based density interpolation method [2] that, away from Wood’s anomalies, leads to well-conditioned linear systems.